Near infrared imaging and spectroscopic observations of the extremely red object (R-K~ 7 mag) CL 0939+4713 B have been obtained with the Near Infrared Camera on the Keck I Telescope of the W. M. Keck Observatory. The imaging shows a slightly elongated structure, while the spectroscopy shows a continuum break that allows us to determine the redshift of z = 1.58 + 0.01/-0.03 for this system. The fits of a range of models to the infrared spectrum suggests that it is predominantly an old (> 10^9 yrs) stellar system that suffers little extinction, while the measurerd R and I magnitudes suggests an age of ~ 3 x 10^8 years. The limit on the equivalent width of any emission line in the infrared spectrum argues that CL 0939+4713 B is not an actively star forming galaxy. This system, though similar in R-K color to HR 10 [also known as J1645+46] (Dey et al. 1999), is much different in morphology and emission line strengths, demonstrating the heterogeneity of extremely red extragalactic objects (EROs) selected on the basis of large values of R-K. Comment: Latex with AAS format, 3 postscript figures, AJ, accepted, includes new I data, new fig 3 and revised interpretation